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Derivative of:
Derivative of x^2+3x
Derivative of x^2-3*x+2
Derivative of (x-2)^2*(x-4)+5
Derivative of (x^2-1)*(x^4+2)
Identical expressions
four *sin(t)^(two)
4 multiply by sinus of (t) to the power of (2)
four multiply by sinus of (t) to the power of (two)
4*sin(t)(2)
4*sint2
4sin(t)^(2)
4sin(t)(2)
4sint2
4sint^2

The derivative of the function/ 4*sin(t)^(2)

Derivative of 4*sin(t)^(2)

The solution

You have entered [src]

     2   
4*sin (t)

$$4 \sin^{2}{\left(t \right)}$$

d /     2   \
--\4*sin (t)/
dt

$$\frac{d}{d t} 4 \sin^{2}{\left(t \right)}$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \sin{\left(t \right)}$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d t} \sin{\left(t \right)}$ :
  1. The derivative of sine is cosine:
    
    $\frac{d}{d t} \sin{\left(t \right)} = \cos{\left(t \right)}$
  The result of the chain rule is:
  
  $2 \sin{\left(t \right)} \cos{\left(t \right)}$
So, the result is: $8 \sin{\left(t \right)} \cos{\left(t \right)}$
Now simplify:

$4 \sin{\left(2 t \right)}$

The answer is:

$4 \sin{\left(2 t \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

8*cos(t)*sin(t)

$$8 \sin{\left(t \right)} \cos{\left(t \right)}$$

Simplify

The second derivative [src]

  /   2         2   \
8*\cos (t) - sin (t)/

$$8 \left(- \sin^{2}{\left(t \right)} + \cos^{2}{\left(t \right)}\right)$$

Simplify

The third derivative [src]

-32*cos(t)*sin(t)

$$- 32 \sin{\left(t \right)} \cos{\left(t \right)}$$

Simplify

The graph

Derivative of 4*sin(t)^(2)